Mathematical Analysis of Viral Replication Dynamics and Antiviral Treatment Strategies: From Basic Models to Age-Based Multi-Scale Modeling

Abstract

Viral infectious diseases are a global health concern, as is evident by recent outbreaks of the middle east respiratory syndrome, Ebola virus disease, and re-emerging zika, dengue, and chikungunya fevers. Viral epidemics are a socio-economic burden that causes short- and long-term costs for disease diagnosis and treatment as well as a loss in productivity by absenteeism. These outbreaks and their socio-economic costs underline the necessity for a precise analysis of virus-host interactions, which would help to understand disease mechanisms and to develop therapeutic interventions. The combination of quantitative measurements and dynamic mathematical modeling has increased our understanding of the within-host infection dynamics and has led to important insights into viral pathogenesis, transmission, and disease progression. Furthermore, virus-host models helped to identify drug targets, to predict the treatment duration to achieve cure, and to reduce treatment costs. In this article, we review important achievements made by mathematical modeling of viral kinetics on the extracellular, intracellular, and multi-scale level for Human Immunodeficiency Virus, Hepatitis C Virus, Influenza A Virus, Ebola Virus, Dengue Virus, and Zika Virus. Herein, we focus on basic mathematical models on the population scale (so-called target cell-limited models), detailed models regarding the most important steps in the viral life cycle, and the combination of both. For this purpose, we review how mathematical modeling of viral dynamics helped to understand the virus-host interactions and disease progression or clearance. Additionally, we review different types and effects of therapeutic strategies and how mathematical modeling has been used to predict new treatment regimens.

Mathematical modeling of interaction between innate and adaptive immune responses in COVID‐19 and implications for viral pathogenesis

“…Mathematical models have been developed to understand the dynamics of viral infections. [16][17][18][19][20] Most of them fall into the category of the target cell-limited model with some variations. The simplest version includes three species: uninfected susceptible target cells (T), which in our case is the surface epithelial cells with ACE2 receptors, located at the respiratory tracks including lungs, nasal and trachea/ bronchial tissues, infected virus-producing cells (I), and the virus particles (V).…”

Mechanistic modeling of the SARS-CoV-2 and immune system interplay unravels design principles for diverse clinicopathological outcomes

“…With no specific cure identified for SARS-CoV-2, investigating the emergent dynamics of the interplay between the infected cells and the components of innate and/or adaptive immune system is likely to help understand the different immunopathology scenarios, and devise effective therapeutic strategies that can curb the disease severity. Mathematical models have been extensively used to describe the dynamics of viral load in patients for HIV, HCV, influenza and Ebola virus (18); however, the integration of immune system dynamics in those frameworks are relatively recent (19)(20)(21). In the context of SARS-CoV-2, a quantitative and predictive framework to understand the dynamics of different possible outcomes of the complex nonlinear interactions among infected cells and immune system remains to be constructed.…”

Trends in mathematical modeling of host–pathogen interactions

“…Only a high investment is effective and leads to the global maximum. For further explanations, see section "Molecular mimicry and crypsis" and Lang et al [77] employed to study the dynamics of bacteria [19,88], fungi [79], viruses (for review, see [8,12,25,52,101,139]), and has also been applied to other areas such as cell division mechanisms (e.g., [53, 63, 65-67, 129, 130]).…”